The use of a flamer is to kill top growth.

You won't be able to flame-kill roots, or the nutlets at their tips, because they are too deep in the soil.

See info at UC
http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7432.html

Here is a link that might be useful: nutgrass, aka nutsedge

As Jean has stated flaming will only kill the top growth, not the tubers in the ground. Aside from using non renewable resources the flame torches are not all that effective and can be quite expensive and in area that have not had adequate rainfall using them may well be banned due to the fire danger they pose.

There are some reports that treating the soil with dry molasses helps the beneficial microbes consume the rhizomes. Organic gardeners swear by it, universities don't mention it.

Either method, organic or chemical, a few applications are needed.

Not all organic gardeners swear by molasses and universities do not mention using molasses because they have not been able to replicate the claims made by some of the proponents of its use. What I have seen tells me that there is no agreement on what molasses does. Some sources swear that you must use dry and others, just as adamant, swear it must be the liquid diluted in water.
Understanding what sedges are, how they evolved, and what conditions they grow best in can help any gardener find ways to eliminate them of that is needed.

Sweeeeeet?

hortster